## vera_ewing one year ago Compare the functions

1. vera_ewing

2. vera_ewing

g(x) right? @freckles

3. freckles

let's play with it together

4. freckles

do you know the range of sin(x) is -1 to 1 ?

5. vera_ewing

Well I'm thinking 2 spots on the number line from -1 to 1. lol

6. freckles

so one of the following will give the min to f -3(-1)+2 -3(1)+2 so what is the min of f? notice the parabola h is in vertex form h=(x-h)^2+k where (h,k) is vertex k gives the min value of the function

7. freckles

and given that what is also the min of h?

8. freckles

the function h

9. freckles

sorry I should have recalled the x-coordinate of the vertex something else

10. freckles

h=(x-c)^2+k where (c,k) is vertex k gives the min value of this function

11. vera_ewing

Ohh wait I totally read the question wrong! It asks for minimum, not maximum!

12. freckles

yep we want the smallest possible y per function

13. vera_ewing

So f(x) is the greatest! Thank you :)

14. vera_ewing

Wait no...hold on I'm redoing it.

15. freckles

you didn't answer my question of the two numbers I mentioned above for f can you tell me the smallest y value

16. freckles

really big hint: $-1 \le \sin(x- \pi) \le 1 \\ \text{ multiply both sides by -3 } \\ 3 \ge -3\sin(x-\pi) \ge -3 \\ \\ \text{ add 2 on both sides } 3+2 \ge -3\sin(x-\pi)+2 \ge -3+2$

17. vera_ewing

Oh they're all the same? So it's D?

18. freckles

yes -3+2 is the min of f and -1 is the min of g and -1 is also the min of h

19. freckles

-3+2=-1=-1

20. vera_ewing

Ohhh okay! Thank you so much! :)